# How do you solve and find the ordered pairs 1/2 x - 2y = 4 and 4y - x = -8?

Aug 18, 2017

Using $x = 4 y + 8 \text{ }$ if you choose values of $y$ you can find the corresponding values of $x$ and hence obtain the ordered pairs.

#### Explanation:

The first equation can be changed into a better form by removing the fraction:

$2 \times \frac{1}{2} x - 2 \times 2 y = 2 \times 4 \text{ } \times$ each term by $2$

$x - 4 y = 8$

the second equation can be rewritten as $x - 4 y = 8$

We therefore see that there is actually only one equation, and as it has two variables, there are many solutions.

Using $x = 4 y + 8 \text{ }$ if you choose values of $y$ you can find the corresponding values of $x$ and hence obtain the ordered pairs.

$y = 0 , \rightarrow x = 8 \text{ } \rightarrow \left(8 , 0\right)$
$y = 1 , \rightarrow x = 12 \text{ } \rightarrow \left(12 , 1\right)$
$y = 2 , \rightarrow x = 16 \text{ } \rightarrow \left(16 , 2\right)$
$y = - 1 , \rightarrow x = 4 \text{ } \rightarrow \left(4 , - 1\right)$
$y = - 2 , \rightarrow x = 0 \text{ } \rightarrow \left(0 , - 2\right)$

IN this way you can generate as many ordered pairs as you need.